Controlled fabrication of nanopores in nanometric solid state materials

ABSTRACT

In a method of forming a nanopore in a nanometric material, a nanopore nucleation site is formed at a location that is interior to lateral edges of the nanometric material by directing a first energetic beam, selected from the group of ion beam and neutral atom beam, at the interior location for a first time duration that imposes a first beam dose which causes removal of no more than five interior atoms from the interior location to produce at the interior location a nanopore nucleation site having a plurality of edge atoms. A nanopore is then formed at the nanopore nucleation site by directing a second energetic beam, selected from the group consisting of electron beam, ion beam, and neutral atom beam, at the nanopore nucleation site with a beam energy that removes edge atoms at the nanopore nucleation site but does not remove bulk atoms from the nanometric material.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.61/452,704, filed Mar. 15, 2011, the entirety of which is herebyincorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with Government support under Contract No.R01HG003703, awarded by the National Institutes of Health. TheGovernment has certain rights in the invention.

BACKGROUND

This invention relates generally to nano-scale fabrication techniques,and more particularly relates to techniques for producing nanopores innanometric solid state materials.

Nanometric solid state materials, that is, solid state materials thatcan exist in equilibrium with only nanometers in thickness, include awide range of materials such as monolayer, few-monolayer, and singlemolecule materials, that are becoming increasingly important for a widerange of applications, including, e.g., electronic, biological, andchemical applications. Many such applications require high-precisionnanoscale features and structures for operation. For example,well-defined nanopores, or nanoscale pores having a diameter less thanabout 100 nanometers, are particularly required for many applicationsdue to the nano-scale of the application itself or the environment inwhich the nanopore is to operate.

For example, nanopore-articulated nanoscale devices are of greatinterest for enabling the localization, detection, and characterizationof molecules such as single DNA molecules or protein molecules. Nanoporefilters and nanoscale holely membranes are likewise important for manycritical biological separation and characterization procedures, as wellas filtration processes. Many other micro-fluidic and nano-fluidicprocessing and control applications similarly rely on nano-scalefeatures in nanometric materials.

To produce a nanoscale structure such as a nanopore in ananometrically-thin material, it is in general required to manipulatethe material with the precision of single atoms. This is in contrast tomost conventional microelectronic fabrication processes, whichcharacteristically only require precision that approaches themicron-scale. But without feature resolution and fabrication precisionat the atomic level, it has in general not been possible to manipulatenanometrically-thin materials in a manner that exploits the particularcharacteristics which emerge at the nano-scale.

High-precision nanoscale processing has historically required aone-at-a-time fabrication paradigm that is often costly and inefficient.Generally, the high-volume, batch fabrication techniques of conventionalmicroelectronic production have been incompatible with nanoscale featureproduction and material manipulation. But without the ability toprecisely, reproducibly, and inexpensively mass-produce nanoscalefeatures such as nanopores, many nanoscale systems cannot be developedfor commercial implementation of many important nanoscale applications.

SUMMARY OF THE INVENTION

There is provided a method and corresponding structures that overcomethe limitations of previous processes to controllably form nanopores. Inone example method of forming a nanopore in a nanometric material, ananopore nucleation site is formed at a location of the nanometricmaterial that is interior to lateral edges of the material by directinga first energetic beam, selected from the group of ion beam and neutralatom beam, at the interior location for a first time duration thatimposes a first beam dose which causes removal of no more than fiveinterior atoms from the interior location to produce at the interiorlocation a nanopore nucleation site having a plurality of edge atoms. Ananopore is then formed at the nanopore nucleation site by directing asecond energetic beam, selected from the group consisting of electronbeam, ion beam, and neutral atom beam, at the nanopore nucleation sitewith a beam energy that removes edge atoms at the nanopore nucleationsite but does not remove bulk atoms from the nanometric material.

With this method, there can be produced a nanometric structure withnanopores. The structure is formed of an impermeable self-supportingnanometric material having a thickness of no greater than about 5 nm. Inthe nanometric material is a plurality of nanopores of at least about1000 nanopores/cm². Each of the nanopores has a diameter that is nogreater than about 10 nm. The plurality of nanopores is monodisperse indiameter with a variation of about ±30%.

This nanometric structure of nanopores, and the method for producing thenanopores, enables a wide range of micro-fluidic and nano-fluidicapplications, including molecular detection and analysis, fluidicfiltering and separation, and fluidic reactions.

Other features and advantages will be apparent the following descriptionand accompanying figures, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of a two-step process for producing a nanopore ina nanometric material;

FIGS. 2A and 2B schematic views of nanometric materials disposed acrossan opening on a support frame and disposed across an array of openingson a support frame, respectively, for carrying out the method of theflow chart of FIG. 1;

FIGS. 3A-3E are schematic side views of a nanometric material as thenanometric material is processed in the steps of the flow chart of FIG.1;

FIG. 4 is a schematic side view of a patterned shielding materialemployed to selectively mask a nanometric material during the nanoporefabrication process of the flow chart of FIG. 1;

FIGS. 5A-5B are schematic views of nanopores formed in nanometricmaterials disposed across an opening on a support frame and disposedacross an array of openings on a support frame, respectively, producedby the method of the flow chart of FIG. 1;

FIG. 6A is a plot of average nanopore radius as a function of electrondose for five experimental nanopores;

FIG. 6B is a plot of nanopore radius as a function of electron dose foreach of the nanopores from which data was taken for the plot of FIG. 6A;

FIG. 7 is a an electron micrograph of a region of graphene in which anarray of nanopores has been formed by the method of the flow chart ofFIG. 1; and

FIG. 8 is a plot of the distribution of nanopore radius for the electronmicrograph of FIG. 7.

DETAILED DESCRIPTION

Referring to FIG. 1, a process 10 for controllably forming one or morenanopores can in general be implemented in a nanometric material withthe two steps shown therein. In a first step 12, at least one nanoporenucleation site is produced at a selected location or at multipleselected locations in a nanometric material for which the controlledfabrication of a nanopore is desired. Then in a second step 14, ananopore is controllably formed at the nucleation site or sites. Each ofthese steps is described in detail below.

This two-step nanopore formation method can be applied to any suitablematerial, but is particularly well-suited for producing nanopores in asolid state material or structure that is characterized by a thicknessthat is nanometric, and for many applications, that is less than about 5nanometers in thickness or less than 3 nanometers in thickness. Suchnanometric materials include, e.g., atomically-thin materials, which ingeneral can be described as materials having a thickness of an atomicmonolayer or a few atomic layers, such as a monolayer, a bilayer, or atrilayer of atoms. A mono-atomically-thick material is herein defined asa material which is one atom in thickness, but need not be atoms of justone element. Atoms of a plurality of different elements can be includedin an atomic layer. The mono-atomically-thick layer can be decorated atthe layer top and/or bottom with heterogeneous atoms and other speciesthat do not lie in the plane of the atoms. Such atomically-thinmaterials include, e.g., two-dimensional free-standing atomic crystals,and other structures having a characteristic unit, like a latticeconstant, that is repeating in two dimensions but not the third.Atomically-thin materials also include non-crystalline materials, suchas glassy materials for which a mono-atomic layer and few-atomic-layerscan be formed. Other example nanometric materials include materials thatare a single molecule in thickness, or that are two or three moleculesin thickness.

Examples of nanometric materials that are well-addressed by the methodinclude graphene, few-layer graphene, fluorographene, graphane, grapheneoxide, hexagonal boron nitride (hexagonal-BN), mono-atomic glasses, andother such materials. Other suitable materials include, e.g., MoS₂, WS₂,MoSe₂, MoTe₂, TaSe₂, NbSe₂, NiTe₂, Bi₂Sr₂CaCu₂O_(x), and Bi₂Te₃. Theseare representative examples of suitable nanometric solid state materialsbut are not limiting; any suitable material in which one or morenanopores are to be formed can be employed.

In the method, a selected nanometric material is provided in a suitableconfiguration for processing to produce one or more nanopores in thematerial. The nanometric material is preferably arranged such that oneor more energetic species can be directed through the material for bothproducing a nanopore nucleation site and for controllably forming ananopore at the site, as explained in detail below. For manyapplications, it can be convenient to arrange the nanometric material ona continuous or discontinuous underlying support structure in anyconvenient orientation that accommodates such nanopore processing. Thesupport structure can be discontinuous, with a topology and materialconfiguration depending on an intended application, and can serve as amasking material, patterned with, e.g., openings of a selected maskingpattern, as described below. The nanometric material in which a nanoporeis to be formed can be, e.g., self-supporting, with support at lateraledges near or at the periphery of the material or at locations within atinterior points, or in another configuration that accommodates thedirection of an energetic species through the nanometric material. Thenanometric material can be synthesized in-position, e.g., in situ in adevice or system configuration, on a selected support structure, or canbe produced or synthesized fully or partially elsewhere and thentransferred to the selected support structure.

The support structure can be provided as any suitable support material,including microelectronic materials and substrates that are electricallyconducting or electrically insulating. The support structure can beprovided as a bulk structure having the composition of the nanometricmaterial or can be provided as a heterogeneous combination of materials.In one example, a support structure is provided as a frame and thenanometric material in which one or more nanopores are to be produced istransferred to the frame.

For example, a silicon substrate can be configured as a support with aframe membrane, e.g., a silicon nitride or other material framemembrane, having one or more apertures in the frame membrane. As shownin FIG. 2A, the nanometric material 16 can be positioned over the framemembrane 18 on the substrate 20. The frame membrane 18 thereby operatesas a support frame around the aperture 22, to enable a self-supportedregion 24 of nanometric material across the aperture 22. As shown inFIG. 2B, this arrangement can be extended to accommodate any number ofdistinct areas of nanometric material that are each suspended 24 in anarray 26, disposed in a support frame 28 across apertures in the framemembrane on a substrate.

In general, the apertures provided in a support frame membrane layer canbe, e.g., rectangular, circular, or of another suitable geometry, andcan be, e.g., between about 5-10 nm and about 200 nm in extent or othergeometry and extent corresponding to a selected nanopore size andlocation, as explained in more detail below. For many applications, itcan be preferred that the aperture in the support frame membrane be atleast about ten times greater than the nanopore to be formed in thenanometric material.

In a further example, a transmission electron microscopy (TEM) grid canbe employed as a support frame for a nanometric material to beprocessed. The TEM grid can be covered with a suitable material, such asa thin amorphous carbon film, and one or more holes, or an array ofholes, can be formed in the film to provide a frame for the nanometricmaterial. Other such arrangements can be employed and no particularsupport or frame is required.

Where the nanometric material is synthesized separately from a supportor frame, the material can be transferred to a support or frame at aconvenient juncture in the synthesis process. In one example, a singlelayer of graphene or few-layer graphene is synthesized and oncesynthesized, is transferred to a selected support structure. In thisexample, the graphene can be synthesized by a suitable process, e.g., achemical vapor deposition process (CVD), or by ion implantation or gasphase synthesis, or by another synthesis technique on a suitablestructure, e.g., a metal layer or substrate, or can be produced byexfoliation of graphite, in the conventional manner. Alternatively, thematerial can be synthesized by a suitable process, e.g., (CVD), ionimplantation, or another synthesis technique, on a suitable structure,e.g., a metal layer or substrate, after which the structure, e.g., ametal layer or substrate, can be converted into a support structure forthe nanometric material by some method, such as a patterned chemicaletching, that does not affect the nanometric material through whichnanopores are subsequently to be formed. No particular nanometricmaterial synthesis process is required, and the nanometric material tobe processed, such as graphene, can be produced in any suitable manner.

In one particularly convenient graphene synthesis process, a nickel orcopper foil can be annealed at a low pressure at a temperature of, e.g.,about 1000° C., for about 10 minutes, under the flow of H₂, and thenalso exposed to flow of CH₄ for about 10 minutes at 1000° C., to grow aregion or regions of graphene. At the end of the 10 minute growth step,the foil is cooled to room temperature with flow of H₂, in a processwhich takes about 2 hours.

If the nanometric material to be processed is produced on a synthesisstructure, such as the graphene synthesis on copper foil just described,then it is preferred that the nanometric material be well-cleaned and,if the nanometric material is to be transferred, that this transferproceed with great care so as not to damage or contaminate thenanometric material. For example, once graphene is synthesized on acopper foil, a suitable piece of graphene on the foil can be punched outand placed on an acid-washed clean glass slide for handling duringtransfer to a support structure. Polymer-based handle materials canalternatively be employed. Where the support structure is, e.g., a TEMgrid having a holely carbon layer, a droplet of deionized water or othersuitable liquid is first placed on the grid layer, and then when broughtinto contact with the graphene, the carbon film is pulled into intimatecontact with the graphene by the receding interface from the liquid. Aglass slide can be placed on top of the TEM grid to enable applicationof force during the contact.

The copper film on which the graphene was synthesized can then be etchedaway from below by, e.g., floating the structure on a suitable etchant,e.g., a copper etchant including FeCl₃ for a suitable duration, e.g., 15minutes for a 25 μm-thick foil. If over-etched, the FeCl₃ will attackthe TEM grid at locations where the grid is exposed at carbon layeredges. Similarly, a polymer film can be removed after placement of thegraphene. Once the copper film or other material is removed, thegraphene as-positioned on the TEM grid can be cleaned, e.g., by floatingthe structure in 1 N HCl, to remove residual iron from the FeCl₃exposure, for about 10 minutes, and then floated in multiple rinses ofdeionized water, for example, about three rinses of ten minutes each, toremove any residual salt, and dried in dry nitrogen.

For many nanometric materials in which a nanopore is to be formed, e.g.,graphene, a high degree of cleanliness is especially preferred,specifically, with regard to graphene, e.g., to reduce the density ofhydrocarbon contaminants such that mobile hydrocarbons on the graphenesurface are substantially reduced. This high degree of cleanliness canbe preferred for aiding in the nanopore formation process. Therefore, ifafter the cleaning and rinsing process described above it is found thatsome amount of surface contamination remains, it can be preferred toconduct a further cleaning step.

In one example cleaning process, contaminants are baked out of thestructure. Here the TEM grid with, e.g., a graphene layer affixed asdescribed above, is transferred to a stainless steel ultra high vacuum(UHV) chamber, and at a pressure of, e.g., less than about 10⁻⁸ Torr,the temperature is ramped to about 300° C. The structure is then bakedfor at least two hours, and preferably overnight, at this temperature.The chamber is then cooled to room temperature slowly, e.g., at lessthan about 2° C./min, with a final chamber pressure at between, e.g.,about 10⁻⁸ T and about 10⁻⁹ T. It is preferred that the structure bestored at room temperature under UHV conditions until use. This processis found to produce a graphene surface that is about 40%-80% free of anycontaminating material, as-observed by TEM viewing.

This example demonstrates that in general, it is preferred to maintainthe nanometric material to be processed under optimally cleanconditions, so that atomic-scale processing of the material is notaffected by contaminants. No particular cleaning or storage processesare required, and those processes best-suited to a selected material arepreferred. With a selected material in place on a support structure, themethod for controllably producing a nanopore can be carried out.

Referring to FIG. 3A, there is shown a nanometric material 30 to beprocessed for the production of nanopores, arranged such that a plane ofatoms 32 of the material is accessible. In this example illustration,one layer of atoms is shown for clarity in explaining the process steps,but such is not required; as explained above, the nanometric materialcan be an atomic multilayer material, a molecular monolayer material, orother nanometric material having a thickness that is generally less thanabout 5 nm.

With the nanometric material in such an arrangement, in the first methodstep, one or more nanopore nucleation sites are formed in the nanometricmaterial at locations that are interior to the lateral edges of thenanometric material, and at which nanopores are to be formed. At such aninterior nanopore nucleation site, some disruption to the continuity ofthe nanometric material is provided that produces edges of material fromwhich edge atoms can be removed for controllably forming a nanopore of aselected size. In other words, due to a disruption in the nanometricmaterial, interior atoms are rendered as edge atoms for removal in theprocess of forming a nanopore. Each nanopore nucleation site istherefore a site at an interior location of the nanometric materialwhere edge atoms are produced by the nucleation site formation.

To form a nanopore nucleation site, some perturbation of the nanometricmaterial atoms is required. In one example of such, a structural defector a single cluster of defects is formed in the nanometric material at alocation interior to lateral edges of the material. The defect can becreated by, e.g., displacing a single atom or small number of atoms inthe material or otherwise disrupting the atomic structure of thematerial. The term “defect” is therefore here intended to refer to anaberration in the atomic bonding structure of the nanometric material.For example, given the nanometric material graphene, a defect can becreated by the removal of one or two atoms from the sp² bonded graphenecarbon network of the material. A sufficient defect exists in thematerial when the number of bonds holding one or more atoms in place isaltered and/or reduced and the defect is relatively stable at a selectedoperating temperature. A one or two atom defect in a hexagonal latticesuch as that of graphene can produce three-four edge atoms at the siteof the defect, and therefore enables the requisite condition of theproduction of edge atoms at an interior nanometric material location fora nanopore nucleation site.

In general, the disruption to the nanometric material at the nucleationsite can be produced in any suitable manner. In one preferable example,an energetic beam of a selected particle species is directed to alocation or locations on the surface of the nanometric material that isselected for production of a nanopore. An ion beam, e.g., a beam ofargon ions, an α-particle beam, a high-energy beta particle beam, anelectron/proton beam, a reactive ion beam created by a plasma, such asan oxygen ion or free radical, or other suitable beam of particles canbe employed. For many applications, an ion beam or beam of neutral atomscan be preferred for ease of use in conventional microfabrication batchprocessing sequences. Example suitable energetic beams include, e.g., Heion beams, hydrogen/proton beams, neon beams, and gallium ion beams,among other suitable species. The energetic beam is not required toitself directly knock out one or more atoms from the nanometricmaterial; the energy delivered by the beam can cause a disruption inatomic bonding that displaces one or more atoms.

Therefore, the energy of the particle beam is characterized as beingabove that energy which provides a minimum particle recoil energyrequired to remove at least one atom from the interior of a nanometriclattice, called the displacement energy, E_(d) ^(bulk). In other words,there must be provided by the particle beam a minimum threshold kineticenergy for the incident particle to displace one or more interior atoms,such that a nanopore nucleation site is produced, or can otherwisedirectly and irreversibly break the bonds of the substituent lattice.

T_(m), the maximum transmitted energy in a single recoil scatteringevent, occurs with a direct head on collision by an incident particlefrom the beam; in a relativistic formulation, this transmitted energy isgiven as:

$\begin{matrix}{T_{m} = \frac{2\;{{ME}\left( {E + {2\; m_{0}c^{2}}} \right)}}{{\left( {M + m_{0}} \right)^{2}c^{2}} + {2\;{ME}}}} & (1)\end{matrix}$where E is the minimum energy of the beam required to create a nanoporenucleation site by removal of an atom, m₀ is the incident particle massat rest, c is the speed of light, and M is the mass of the atom to beremoved from the lattice.

A simple estimate for the displacement energy, E_(d) ^(bulk), of aparticular atom within the bulk lattice of a given material is obtainedby summing the energy of all of the bonds in the lattice, based on,e.g., tabulated values. For example, the estimated displacement energyfor a carbon atom in a monolayer of graphene using this method is E_(d)^(bulk)≈6.4 eV×3=19 eV, a value that is reasonably close to the measuredvalues for graphene in bulk graphite of 20-21 eV. Note that thedisplacement energy is a function of the angle between the incident beamand the plane of the atoms in the lattice. In this analysis, it can beassumed that the beam is substantially perpendicular to the nanometricmaterial plane. The minimum energy of the beam, E, to create a defectcan then be calculated using Expression (1) above with T_(m) set to thedisplacement energy, E_(d) ^(bulk), plus some margin of error to accountfor the uncertainty of the beam energy in the apparatus and theapproximate nature of the calculation, say 50%.

For a beam of low energy ions, having a kinetic energy that is much lessthan the rest energy, employed to produce nanopore nucleation sites, inwhich case a non-relativistic analysis applies, Expression (1)simplifies to:

$\begin{matrix}{E = {T_{m}\frac{\left( {m_{0} + M} \right)^{2}}{4\; m_{0}M}}} & (2)\end{matrix}$

Based on this expression, it can be specified that for a beam oflow-energy ions, an appropriate beam energy to remove atoms forproducing in a nanometric material nanopore nucleation sites, E_(nuc),including a 50% margin of error, is given as:

$\begin{matrix}{E_{nuc} \geq {{1.5 \cdot E_{d}^{bulk}}\frac{\left( {m_{0} + M} \right)^{2}}{4\; m_{0}M}}} & (3)\end{matrix}$

Based on this Expression (3) above, and given estimates of E_(d) ^(bulk)using the method above, there can be determined the requisite beamenergies for a beam of interest. For example, given an argon ion beam,Table 1 below specifies the requisite beam energy for nanoporenucleation site formation for three nanometric materials.

TABLE 1 Bulk atom displacement Argon beam energy Target material energyestimate E_(d) ^(bulk) for nanopore nucleation E_(nuc) Graphene 21eV >44 eV Boron nitride B = 15 eV N = 14 eV >34 eV Molybdenum Mo = 10 eVS = 5.2 eV >19 eV disulfide

In most metallic and semi-metallic materials which are not subject toother forms of irradiation-induced damage, below the requisite beamenergy, impinging beam particles do not damage a pristine lattice, evenafter very large doses of irradiation. For example, a pristine graphenelattice can withstand a dose of >10⁹ electrons/nm² at 80 keV without anydamage to the lattice.

For many applications, the minimum incident beam energy required toproduce nanopore nucleation sites can be determined empirically. Forexample, a selected nanometric material can be irradiated with anenergetic beam at an initial energy for which T_(m)˜5 eV. Then theenergy of the beam can be slowly increased until there is evidence thatatoms of the nanometric material are being removed by the beam. Thisexperiment can be conducted all on one nanometric material sample if adetector is available to in situ detect recoiling atoms from thematerial. Alternatively, this experiment can be conducted on severaldifferent nanometric material samples, with stepwise increases in energyand a post imaging step to determine that atoms were removed. Once anappropriate energy is determined for a given incident particle/materialcombination, then the dose required to remove a particular number ofatoms per unit area can also be measured and then specified a priori tocreate a desired number of nucleation sites per unit area on a selectednanometric material.

Once a beam energy is selected, then the duration of exposure of thenanometric material to the energetic beam is selected to produce thedesired nanopore nucleation site. Specifically, the duration of timeduring which the energetic beam is directed at the nanometric materiallocation or locations is set to impose a dose of particles from the beamthat produces a nanopore nucleation site. Preferably, the nanoporenucleation site is controlled to be of atomic-scale dimensions. Thenucleation site, for most applications, can be therefore be specified asa location in the nanometric material that is interior to lateral edgesof the nanometric material and at which about five or less interioratoms have been removed by the energetic beam. The dose of particlesfrom the energetic beam thereby produces a nucleation site at theinterior of the nanometric material at which five or less interior atomshave been removed, producing a plurality of edge atoms at the site. Forexample, given the nanometric material graphene, an argon ion beam doseof about 1×10¹³ Ar⁺/cm² at a beam energy of about 3 keV can be employedto produce nanopore nucleation sites in the graphene. With this controlof nanopore nucleation site production, the continuity of the nanometricmaterial is disrupted by the removal of five or less atoms, at aninterior location, so that interior atoms at the site are rendered asedge atoms, for formation of a nanopore.

Under some processing conditions and for some materials such asgraphene, there is demonstrated a resistance by the nanometric materialto form a nanopore nucleation site at room temperature, even above theknock on threshold, due to mobility of atoms in the nanometric material.As a result, it can be preferred to experimentally determine thecharacteristic tendency of a selected nanometric material to bedisrupted at a selected operating temperature, and to cool the materialduring irradiation, if necessary, to preserve the disruption in thematerial. For example, graphene cooled to 149 K and irradiated by 3 keVAr⁺ is damaged with defects appropriate for making nanopores butgraphene that is irradiated by 3 keV Ar⁺ ions at 300 K shows far fewernanopore nucleation sites. Specifically, at 300 K the probability that asingle argon ion will produce a defect for nucleation of a nanopore is <1/10^(th) of that probability at 148 K.

It is therefore desirable to cool the nanometric material to atemperature that reduces surface ad-atom diffusion such that mobileatoms cannot replace atoms removed by the incident energetic beam. Basedon measurements of irradiation of graphite, this temperature isunderstood to be in the range of about 160 K-200 K for graphene. As aresult, a processing temperature below about 200 K can be preferred, anda temperature below about 160 K can be more preferred, with lowertemperatures improving the efficiency of nanopore nucleation sitecreation. It is to be understood that this temperature can vary fordifferent nanometric materials. The appropriate processing temperaturefor a given nanometric material can be determined empirically byreducing the temperature of the nanometric material during energeticbeam irradiation until the nanopore nucleation site creation efficiencybecomes comparable to the cross section for atomic displacement.

The production of a nanopore nucleation site in a nanometric material byan incoming particle is schematically shown in FIG. 3B. A particle 34 ina beam of particles is directed 36 to the nanometric material. Thecollision of each such particle 34 with atoms 32 of the material canremove one or a number of atoms in a single collision, with the removedatoms 40 taken out of the nanometric material structure as the particletraverses and exits 38 the nanometric material. As shown in FIG. 3C,this results in a changed nanometric material 42, now including ananopore nucleation site 44 having an edge at which edge atoms can beremoved.

The dose of the nanopore nucleation-generating particles can becontrolled such that only one isolated material disruption or onecluster of disruptions is created at a nanopore site of a nanometricmaterial or at each of a plurality of sites of interest. This can beachieved, e.g., using a calibrated source for an accurately-controlledbeam irradiation duration, or for a liquid environment, e.g., feed-backcontrol from ionic currents that can be provided, for example, bymonitoring ionic flow through a material, such as a sheet of graphene,that is suspended so as to separate two ion containing solutions, one ofwhich is biased with respect to the other.

With this control, the nanometric material being processed can bepositioned with respect to the nanopore nucleation site-generatingparticles so that one material disruption or one cluster of disruptionsis produced at a location that is specified for formation of a nanopore,or so that an array of material disruptions is produced across thematerial for formation of an array of nanopores in the material. Wheremore than one nanopore is desired, a physical masking arrangement can beemployed to expose only those locations of the nanometric material atwhich nanopores are to be formed to the disrupting environment. Here,e.g., as shown in FIG. 4, a patterned shielding mask 60 of sufficientthickness and of appropriate material to prevent penetration ofparticles can be positioned in front of the nanometric material 30 sothat a source of particles, whether focused or unfocused, as shown, willirradiate only a selected region or regions of the nanometric material.

Many materials have stopping power to a beam of ions that is sufficientfor operation as a relatively thin ion beam mask. For example, a thinfoil of Al, Au, Si, Cu, SiO₂, SiN_(x), nylon, Teflon, or other suitablematerial can be employed. In a further example, it is found that alphaparticles resulting from radioactive decay have a very low penetrationdepth, a few centimeters of air, and therefore can be stopped by afew-micrometer layer of aluminum foil. Such a foil layer can be preparedwith holes located in a pattern that matches the position or positionsof the desired finished nanopores. The foil can then be used as aprotective layer between the nanometric material being processed byincoming defect-generating particles and the source of the incomingdefect-generating particle.

In an alternative embodiment, a highly focused particle beam, e.g., afocused gallium ion beam, or other focused beam such as an electronbeam, at suitable energy as described above, can be directedspecifically to locations at which a nanopore nucleation site is to beproduced in the formation of a nanopore, in a sequential manner. Thissequential site-irradiation technique eliminates the need for a physicalmask while at the same time producing defects with nanometer accuracy inposition.

The source of the particles to be employed for forming a nanoporenucleation site need not be dry and instead can be provided in anaqueous solution, or other suitable environment. For example, an aqueoussolution can be provided as a 7% (w/w) solution of uranyl acetate indistilled water. Because a small percentage of any uranium solution isUr²³⁸, the solution will emit alpha particles for impinging on amaterial placed in the solution.

Referring now to FIG. 3D, in the second step of the process, there iscontrollably formed a nanopore at the nanopore nucleation site. In thisnanopore formation step, the nucleation site 44 is perturbed in a mannerthat controllably produces a nanopore without damaging the nanometricmaterial surrounding the nucleation site. This nanometric materialsurrounding the nucleation site is herein defined as that nanometricmaterial that was not disturbed by the nucleation site-generatingprocess of the first step in the method.

In one example process, as shown in FIG. 3D, a beam 45 of particles 47having an energy that is below the energy threshold for knock-on damagein the undisturbed nanometric material, i.e., below the threshold forremoval of bulk atoms from the nanometric material, is directed normalto the plane of atoms 32 of the nanometric material. These energeticparticles 47 controllably remove only those edge atoms 50 at thecircumference, or perimeter, of the nanopore nucleation site 44 whileretaining the integrity of the remaining nanometric material by notremoving bulk atoms from the interior locations of the nanometricmaterial that are not at the nanopore nucleation site.

As shown in FIG. 3D, an incoming particle 52 striking the edge of thenucleation site 44 can remove an edge atom 50 at the periphery of thesite, while an incoming particle 54 that strikes the nanometric materialat a location away from the nanopore nucleation site does not causeremoval of a bulk atom from the interior of the nanometric material. Asthe irradiation of the nanometric material is continued, additional edgeatoms are removed at the periphery of the nucleation site, while awayfrom the nucleation site the nanometric material remains intact and bulkatoms are not removed. Absent any source of atoms to fill in those edgeatoms that are removed, a nanopore develops at the nanopore nucleationsite. The nanopore geometry therefore is directly influenced by theevolving state of edge atom removal at the nanopore nucleation site. Thenanopore may be generally circular, but can be any selected geometry,and can include asperities or other non-continuous geometric features.

The diameter of the nanopore increases in direct proportion to the doseof removal environment, e.g., electrons or ions per unit area, thusoffering very accurate control of the area of the nanopore. Given thatthe nanopore can have an irregular geometry, e.g., that is non-circular,the term diameter can refer to, e.g., the largest extent across thenanopore. Beam irradiation of the forming nanopore can be controllablystopped when the nanopore reaches the desired size. As shown in FIG. 3E,formation of a nanopore 55 is then completed in the nanometric material30. The nanopore can be characterized by a diameter or largest extentbetween edges, that ranges from, e.g., between about 3 Å and about 1000Å.

FIG. 5A schematically presents an example of the resulting nanopore 70produced in a nanometric material 16 that is self-supported and thatextends across an opening in a frame 18 on a substrate 20. FIG. 5Bsimilarly schematically presents an example of an array of nanopores 75produced simultaneously in a self-supported nanometric material 24, on aframe 28 and substrate 29 with distinct selected regions of nanometricmaterial 76 in which nanopores are provided in a controllable fashion.

An ion beam, electron beam, or other suitable beam of energy that can bedirected to the plane of a nanometric material can be employed in thisnanopore formation step. For many applications, a low-energy ion beamthat is unfocused on the scale of the nanopore can be preferred, giventhe production of nanopore nucleation sites also by an ion beam. Anall-ion beam process enables large-scale production in an efficient,practical manner, with the entire process conducted in a singleinexpensive apparatus in which large device areas and/or many devicescan be processed in parallel.

Because the beam is employed in the nanopore formation step toselectively remove atoms only from the edge of the nanopore nucleationsite, the energy of the incident beam is tuned specifically to thiscondition. Particles of the beam therefore preferably are characterizedby an energy that is greater than that required to remove an atom at theedge of the nanopore but less than that which would remove a bulk atomfrom the interior of the material. To quantify this condition, there canbe defined an edge atom displacement energy, E_(d) ^(edge), given as theenergy required to remove an atom from the edge of a nanometricmaterial. An incident particle beam should have an energy such that themaximum transmitted energy, T_(m), in a single scattering event, asexpressed in Expression (1) above, is set as:E _(d) ^(edge) <T _(m) <E _(d) ^(bulk)  (4)

The value of E_(d) ^(edge), if unknown, can be estimated by summing thebonding energies for an atom at an edge of the lattice of the nanometricmaterial, using, e.g., tabulated values. Considering, e.g., a grapheneedge atom, which on average has two bonds to the bulk lattice, thenE_(d) ^(edge)≈6.4 eV×2=13 eV, a value that is reasonably close to theexperimentally-measured value of 14.1 eV. Based on this value, if thereis employed an energetic beam having an energy such that T_(m)≅(E_(d)^(bulk)+E_(d) ^(edge))/2=(19+13)/2=16 eV, then only the atoms at theedge of a nanopore nucleation site in graphene will be removed. Thisvalue can be further tuned empirically to optimize the removal of atomsat the edge of a nanopore nucleation site without creating additionaldefects in the bulk lattice.

Once one has selected an appropriate energy for the beam then the rateof edge atom removal can be measured, either during irradiation if adetector is available in situ to detect the particles transmittedthrough the membrane or on several samples with stepwise increases indose followed by imaging to determine the number of atoms removed perincident particle dose. The irradiation of a nanopore nucleation site bythe energetic beam is continued until a sufficient beam particle dosehas removed a sufficient number of edge atoms at the nanopore nucleationsite to form a nanopore of selected size. For example, given the use ofan 80 keV electron beam to form nanopores at nanopore nucleation sitesin graphene, then an electron beam fluence of about 3×10³ e⁻/Å²/s, canform a nanopore having a 20 Å radius in about two hours. Thus, theenergetic beam dose can be a priori selected to produce a correspondingnanopore size.

As an alternative to dry beam processing, if it is desirable to maintaina nanometric material in a liquid solution, a selected solution can beemployed to preferentially react with nanopore nucleation sites on thenanometric material. For example, given a graphene material, then nitricacid or other solution chemistries that are known to preferentiallyreact with disturbed nanometric sites, such as non-six-membered carbonring lattice structures, or the edges of a graphene lattice, can beemployed to form a nanopore at a nanopore nucleation site in thegraphene. Continued chemical exposure with, for example, nitric acid,can effect controlled removal of atoms from only the disturbed site andthe subsequently-formed nanopore edge, while leaving the rest of theundisturbed graphene intact. Such chemical treatment can be preferredfor feed-back control of the nanopore size by monitoring ionic flowthrough the growing nanopore in the sheet of graphene. Once a nanoporeof selected size has been produced, the reaction can be terminated by,e.g., introduction of a neutralizing base species, such as KOH, into thesolution, or provision of another basic solution. Alternatively, anautomatically operative set of solutions can be employed, e.g., with anacid on one side of the nanometric material, to etch a nanopore in thematerial, and a basic solution on the other side of the nanometricmaterial to neutralize the acid and stop the nanopore formation process.The ratio of acid molarity to basic molarity can here be specified todetermine the nanopore size at which etching ceases.

It is found that like nanopore nucleation site formation, nanoporeformation itself can be influenced by temperature. For example, duringirradiation at room temperature, atoms can diffuse around the insideedge of the nanopore, affecting the overall nanopore shape. Controllingthe temperature of the nanometric material during irradiation cantherefore be preferred to enable an ability to increase or decrease theamount of material diffusion that occurs at the evolving nanopore edge,and thus control the shape of the nanopore. For many applications, ananopore formation temperature of between about 78 K and less than about300 K or less than about 200 K, can be preferable.

The shape of an evolving nanopore can also be controlled by using afocused electron beam, such as that in a scanning transmission electronmicroscope (STEM), and slowly moving the focused beam area to etch awayonly particular portions of the edge of the nanopore. The nanopore shapecan also be modified by exposing the nanometric material to an increasedtemperature after irradiation to adjust the shape, e.g., roundness, orother aspect of the nanopore.

For many applications, it can be preferable to empirically characterizethe nanopore formation process so that a nanopore diameter specified apriori can be produced with a corresponding beam dose. In one method fordetermining such, there is experimentally determined the nanopore sizethat results as a function of total dose, e.g., total electron dose. Forexample, for the nanometric material graphene, the edge of graphene ischaracterized by a distinct defocused fringe pattern in a transmissionelectron micrograph (TEM). The radius of a nanopore in a graphene regioncan be determined by selecting the center of the nanopore andintegrating the image intensity over azimuthal angles as a function ofradius, dividing by the circumference at that radius as a normalization.The point of inflection of the defocused edge fringe can be identifiedas the average radius of the nanopore.

For many applications, it can be convenient to image the nanopore duringits formation to obtain the requisite radius data. For example, givennanopore formation in graphene, TEM exposure to a defocused electronbeam at an energy of about 80 keV enables formation of a nanopore at ananopore nucleation site and provides imaging capabilities for real-timeimaging of the nanopore evolution. Similarly, the nitric acid-basednanopore formation process described above enables feedback controlprovided by the monitoring of ionic current flow through an evolvingnanopore.

However nanopore radius data is collected, once such is available, therecan be determined the correlation between dose and nanopore radius forgiven nanometric material and beam irradiation conditions andtemperature, such that an essentially automated approach to formation ofa nanopore of prespecified diameter can be enabled. The circumference ofa nanopore can be specified as increasing linearly with dose as nanoporeedge atoms are removed. For a circular nanopore, this can be specifiedfor the nanopore radius, r, as r=Md where d is the dose, e.g., inelectrons/unit area, and where M is the measured constant ofproportionality.

With this specification for obtaining a selected radius, there isenabled the ability to form large populations of monodisperse nanoporesin a selected nanometric material. Such nanopore populations can beparticularly important for, e.g., microfluidic applications such asfiltering, molecular analysis, and chemical reactions. In general, toenable such applications, the nanometric material is impermeable to aspecies that is intended to be passed through the nanopores. Thenanopores can be formed in an array that is ordered or in a randomconfiguration, and that is monodisperse in diameter. The termmonodisperse is herein meant to refer to a monodispersity in diameter ofa plurality of nanopores in a population of nanopores, with a variationof about ±30%. This monodispersity can be achieved in a nanometricmaterial with the two-step nanopore formation method to produce, e.g., aplurality of nanopores each having a diameter of, e.g., no greater thanabout 10 nm, e.g., no greater than about 4 nm, in a population of, e.g.,about 1000 nanopores/cm² having a monodispersity in diameter with avariation of about ±30%. In a further example, this monodispersity canbe achieved in a nanometric material for a selected number of nanopores,e.g., at least about 50 nanopores, each having a diameter of, e.g., nogreater than about 10 nm, e.g., no greater than about 4 nm, having amonodispersity in nanopore diameter with a variation of about ±30%.

This nanopore formation control can be easily exploited to repeatedlyand reliably form populations of nanopores that meet specificrequirements for a range of applications. Whether one nanopore, a smallplurality of nanopores, or a large population of nanopores is needed,the two step nanopore formation process enables atomic-scale control ofthe nanopore formation process.

Example 1 Formation of a 20 Å Nanopore in Graphene

The nanometric material graphene was synthesized by chemical vapordeposition on a 25 μm-thick polycrystalline copper substrate (Aesar).The substrate was annealed at low pressure under continuous H₂ flow at1000° C. for ˜10 minutes, exposed to an additional flow of CH₄ for ˜10min at 1000° C. to grow the graphene, and then allowed to cool back toroom temperature under continuous gas flow, requiring about 2 hours.After growth, the graphene was transferred to gold TEM grids covered ina thin amorphous carbon film with regular arrays of micron scale holes(Quantifoil, Au 1.2/2.0). A drop of deionized water was placed on theTEM grid and then the grid was placed on the graphene, which was pulledinto contact with the graphene by the receding interface from the waterdroplet. The copper was then etched away from below by floating thestructure on top of FeCl₃ copper etchant (Transene). Once etched, thesample was then floated in 1N HCl to remove residual iron from the FeCl₃and then floated in three rinses of deionized water to remove anyresidual salt, and dried in dry nitrogen.

At this point, several of the structures still contained variableamounts of surface contamination that likely formed during the growthprocedure, so bake-out of the contamination was conducted. The TEM gridswere transferred to a stainless steel UHV chamber that was just baked to400° C., evacuated to <10⁻⁸ torr, and then baked overnight at 300° C.The final pressure in the chamber after bake-out was ˜5×10⁻⁹ torr. Thestructures were then stored in this chamber under UHV at roomtemperature until use.

To produce isolated nanopore nucleation sites in the graphene lattice,the structures were transferred to an ion sputtering system capable ofirradiating samples at various temperatures with a known dose of ionsunder UHV conditions. The beam fluence was calibrated by measuring thecount rate of the beam limited by an aperture of known size. Eachstructure was inserted through a load-lock mechanism and then cooled tothe base temperature of 148 K. The residual pressure in the chamber was<10⁻⁹ torr, and the residual partial pressures of species up to 100 AMUwere monitored with an in situ residual gas analyzer (Ametek) to ensurethat there were no detectable hydrocarbons, water, or other reactivespecies in the chamber during irradiation.

To produce nanopore nucleation sites in the graphene, the positive argonion beam was pulsed with a duty cycle of 500 msec on-500 msec off untilthe structure reached the desired dose that was computed to produce therequisite disruption to the graphene, here 1×10¹³ Ar⁺/cm² at 3 keV. Thesample was cooled to 149 K to reduce the probability of diffusion ofatoms on the surface of the graphene, thus preventing atom movement fromimmediately repairing newly-formed nanopore nucleation sites in thelattice. Theoretically, each ion that transits the graphene has theability to remove one or two atoms from the lattice, and the sputteryield for an argon ion at 3 keV on graphene is estimated to be of theorder 0.5 carbon atoms removed per incident argon ion. After ion beamexposure to form nanopore nucleation sites was complete, the structurewas then warmed back to 300 K and transferred to a small UHV chamber forstorage.

The structure was then transferred to a transmission electron microscope(TEM) for controllably producing a nanopore. With the TEM, a singlecrystalline grain of graphene was identified using selected areadiffraction, and the grain was verified as single-layer from relativediffraction peak intensities at 0° tilt. A selected region in the grainat which an ion-beam induced nanopore nucleation site existed was thencontinuously irradiated by a parallel, 80 keV electron beam, and imagesof the process were acquired at 30 or 60 second time intervals. Thenanometric material structure was nominally maintained at roomtemperature within the electron microscope. The irradiation wasperiodically stopped as the nanopore diameter grew, to verify thecontrol of the process. At an electron beam fluence of 3×10³ e⁻/Å²/s, itwas found that a nanopore of 20 Å radius was formed in about two hours.

Before and after the electron beam irradiation, the electron beamcurrent was measured with a Faraday cup integral to the structure holder(Gatan single-tilt holder), attached to a pico-ammeter (Keithley 2400),and the beam area was measured directly from an image of the graphenegrain irradiation area, which was limited by the condenser aperture. Thelargest contribution to systemic error is likely the beam currentmeasurement, due to backscattering and secondary electron loss out ofthe 0.49 steradians of exit angle subtended by the entrance to theFaraday cup.

All other systematic biases were estimated to contribute <1% error tocross section measurements. Residual pressure was less than 1.3±10⁻⁷torr, and a liquid nitrogen anti-contamination device in close proximityto the structure protected it from contamination and residual watervapor in the column during electron irradiation. Objective lensaberrations were corrected to 3rd order using a post objective hexapolecorrector (CEOS), aligned to have C₁≅+300 Å, C₃≅−=−1 μm, and all otheraberration coefficients minimized. Images were zero-loss filtered to ˜1eV about the primary energy of 80 keV using the in-column omega filterto improve high-resolution phase contrast by removing the inelasticelectrons. Micrographs were collected on a Gatan Ultrascan 4k camera ora TIVPS 4k camera at a nominal instrument magnification of 400-800 kX orcamera length of 450 mm for selected area diffraction.

Example 2 Characterization of Graphene Nanopore Radius Correlation toDose

To quantify the correlation between the radius of a nanopore in grapheneas a function of dose of electrons employed to produce that nanoporeradius, the two-step nanopore formation process of Example 1 wasconducted, here with an ion beam dose of 1×10¹³ Ar⁺/cm² for producingnanopore nucleation sites in the graphene, and with an electron fluenceof 3190±50 e⁻/Å²/s for producing a nanopore at the sites. Sequentialmicrograph images containing multiple growing pores were obtained andanalyzed by integrating the micrograph intensity over azimuthal anglesas a function of radius, dividing by the circumference at that radius.The point of inflection of defocus at edge fringe was identified as theaverage radius of the nanopore.

Micrographs were drift corrected using a cross correlation algorithm andpost-processed in ImageJ, with a low-pass filter to a 1.0 Å cutoff,adjusted to 8 bits of linear contrast about the mean intensity value,and cropped to the region of interest. The total exposure time in aparticular micrograph was then determined by subtracting the image timestamp from the exposure start time. The exposure time multiplied by thebeam fluence was then taken as the dose for a particular micrograph, asthe beam current varied by <2% during the course of the experiment.

FIG. 6A is a plot of the resulting data for nanopore radius as afunction of electron dose, where each data point is derived from theazimuthal integral of a nanopore image in a sequence of acquired images.Analysis on four additional nanopores produced under the same conditionsresulted in measurement of random error in the slope of radius versusdose, and is identified by the grey region. The black line is a bestlinear fit to the trajectories for the total of five nanopores analyzed.FIG. 6B is a plot of each of the five sets of nanopore radius data, hereprovided separately.

Based on this experimental data, it is found that the circumference ofthe nanopore increased linearly with dose as nanopore edge atoms wereremoved. The average total cross section, σ_(e), for removing thenanopore edge atoms was determined from the experimental data, based onthe slope and the density of carbon atoms at the nanopore edge. Theresult is 8.9±0.4×10⁻²⁴ cm², where the error is the standard deviationfrom 5 measurements. Using conservative estimates of the systematicerror in the measurement technique, the upper and lower bounds on thisvalue are 9.4 and 7.5×10⁻²⁴ cm² respectively.

Example 3 High-Density Nanopore Formation in Graphene

Following the process of Example 1, a graphene region of 6.27×10⁵ Å² wasexposed first to a 3 keV beam of argon ions to impose a dose of 1×10¹³Ar⁺/cm² in the formation of nanopore nucleation sites, and then exposedto an electron beam to impose a dose of 9.7×10⁶ e⁻/Å² to form nanoporesat the nucleation sites. FIG. 7 is a micrograph of the resultingstructure, identifying 32 nanopores, as indicated by arrowheads. Thelocations of some of the smaller and larger nanopores in the image weredetermined by looking at preceding and subsequent images in a series ofimages. The resulting nanopore density corresponds to 5.1×10¹¹nanopores/cm². This correlates with the ion beam dose of 1×10¹³ Ar⁺/cm²as each 3 keV Ar⁺ having a probability of about 5% of nucleating ananopore under these irradiation conditions.

FIG. 8 is a plot of nanopore radius distribution for the nanopores shownin the image of FIG. 7. The nanopore radius distribution is found to besharply peaked. This data demonstrates that the nanopore formationprocess is particularly effective at producing monodisperse nanopores.Monodisperse is here defined as a distribution in radius of ±30%.

Example 4 Comparative Example of Electron Beam Irradiation withoutNanopore Nucleation Site Production

An experiment was conducted to confirm that nanopore nucleation sitesynthesis is required to enable nanopore formation in accordance withthe method described above. In the control experiment, a graphene regionof 6.27×10⁵ Å² was prepared in the manner of Example 1, corresponding tothe graphene region extent of Example 3. The synthesized graphene wasexposed to an 80 keV electron beam to impose an electron dose of 9.7×10⁶e⁻/Å² in the manner of Example 3. This electron beam energy meets therequirement of the two-step nanopore formation method in that 80 keV islower than the required to remove bulk graphene atoms, in the interiorregion of the graphene material. No ion beam irradiation step to firstform nanopore nucleation sites was conducted. After the electron beamdose was produced, the graphene was examined, and was found to includeno nanopores. This confirms that without the formation of nanoporenucleation sites, the electron beam dose does not form nanopores.

This description and examples demonstrate that the nanopore nucleationand formation process provides an elegantly uncomplicated, efficient,and repeatable process that can be implemented on a large scale overlarge areas and many devices. Many applications requiringmass-production of nanopores can therefore be implemented in a practicalmanner and reasonable cost.

It is recognized, of course, that those skilled in the art may makevarious modifications and additions to the processes of the inventionwithout departing from the spirit and scope of the present contributionto the art. Accordingly, it is to be understood that the protectionsought to be afforded hereby should be deemed to extend to the subjectmatter of the claims and all equivalents thereof fairly within the scopeof the invention.

We claim:
 1. A method of forming a nanopore in a nanometric material,the method comprising: forming a nanopore nucleation site in ananometric material, the nanometric material having a thickness that isless than about 5 nanometers, the nanopore nucleation site being formedat a location of the nanometric material that is interior to lateraledges of the nanometric material by directing a first energetic beam,selected from the group consisting of ion beam and neutral atom beam, atthe interior location with a beam energy that is at least that beamenergy which provides at the nanometric material a bulk atomdisplacement energy of E_(d) ^(bulk), that can remove bulk atoms fromthe nanometric material, for a first time duration that imposes a firstbeam dose which causes removal of no more than five interior bulk atomsfrom the interior location to produce at the interior location ananopore nucleation site having a plurality of edge atoms; and forming ananopore at the nanopore nucleation site by directing a second energeticbeam, selected from the group consisting of electron beam, ion beam, andneutral atom beam, at the nanopore nucleation site with a beam energythat is less than that beam energy which provides at: the nanometricmaterial a bulk atom displacement energy of E_(d) ^(bulk), to therebyremove edge atoms at the nanopore nucleation site but not remove bulknanometric material atoms that are not at the nanopore nucleation site.2. The method of claim 1 wherein the second energetic beam is directedat the nanopore nucleation site for a second time duration that imposesa second beam dose which causes removal of a plurality of edge atoms toform a nanopore in the nanometric material having a diameter less thanabout 1000 Å.
 3. The method of claim 1 wherein the nanometric materialis selected from the group consisting of graphene, few-layer graphene,fluorographene, graphane, and graphene oxide.
 4. The method of claim 1,wherein the nanometric material is selected from the group consisting ofhexagonal-BN, mono-atomic glasses, MoS₂, WS₂, MoSe₂, MoTe₂, TaSe₂,NbSe₂, NiTe₂, and Bi₂Te₃.
 5. The method of claim 1 further comprisingfirst disposing on the nanometric material a patterned masking materialthat includes openings through which the energetic beams can be directedat the nanometric material.
 6. The method of claim 1 wherein the firstenergetic beam comprises an ion beam selected from the group consistingof argon, gallium, neon, hydrogen/proton, and helium ion beams.
 7. Themethod of claim 1 wherein the first energetic beam and the secondenergetic beam each are ion beams.
 8. The method of claim 1 wherein thefirst energetic beam is an ion beam and the second energetic beam is anelectron beam.
 9. The method of claim 1 wherein forming a nanoporecomprises forming a nanopore having an extent that is between about 3 Åand about 1000 Å.
 10. The method of claim 1 further comprisingdetecting, during direction of the second energetic beam to thenanometric material, beam particles that are transmitted through aforming nanopore, and controlling the second energetic beam in responseto the detection to form a nanopore of a selected extent.
 11. The methodof claim 1 further comprising maintaining the nanometric material at atemperature no greater than about 300 K when the first energetic beam isdirected at the nanometric material.
 12. The method of claim 11 furthercomprising maintaining the nanometric material at a temperature nogreater than about 200 K when the first energetic beam is directed atthe nanometric material.
 13. The method of claim 1 further comprisingmaintaining the nanometric material at a temperature no greater thanabout 300 K when the second energetic beam is directed at the nanometricmaterial.
 14. The method of claim 13, further comprising maintaining thenanometric material at a temperature no greater than about 200 K whenthe second energetic beam is directed at the nanometric material. 15.The method of claim 1 wherein forming a nanopore nucleation sitecomprises forming an array of nanopore nucleation sites, and whereinforming a nanopore at the nanopore nucleation site comprises forming ananopore at each site in the array of nanopore nucleation sites.
 16. Themethod of claim 15 wherein forming an array of nanopore nucleation sitescomprises forming a nanopore nucleation site array having a density ofat least about 1000 nanopore nucleation sites/cm², and wherein forming ananopore comprises forming a nanopore at each site in the array ofnanopore nucleation sites.
 17. The method of claim 1 further comprisinga first step of disposing the nanometric material on a support structurefor processing by the first and second energetic beams.
 18. The methodof claim 17 further comprising a first step of synthesizing thenanometric material and transferring the synthesized material to thesupport structure.
 19. The method of claim 17 wherein the supportstructure includes an aperture across which the nanometric materialextends.
 20. The method of claim 19 wherein the support structurecomprises a transmission electron microscopy grid.